Grégory Chatel ; Viviane Pons - Counting smaller trees in the Tamari order

dmtcs:12824 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12824
Counting smaller trees in the Tamari orderArticle

Authors: Grégory Chatel 1; Viviane Pons 1

We introduce new combinatorial objects, the interval-posets, that encode intervals of the Tamari lattice. We then find a combinatorial interpretation of the bilinear form that appears in the functional equation of Tamari intervals described by Chapoton. Thus, we retrieve this functional equation and prove that the polynomial recursively computed from the bilinear form on each tree $T$ counts the number of trees smaller than $T$ in the Tamari order.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: binary trees,Tamari lattice,Tamari intervals,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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